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arXiv · 1809.10354

Geometric Transformation of Finite Element Methods: Theory and Applications

M. Holst·M. Licht
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Abstract

We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson problem over a curved physical domain to a Poisson problem over a polyhedral parametric domain. This greatly simplifies both the geometric setting and the practical implementation, at the cost of having globally rough non-trivial coefficients and data in the parametric Poisson problem. Our main result is that a recently developed broken Bramble-Hilbert lemma is key in harnessing regularity in the physical problem to prove higher-order finite element convergence rates for the parametric problem. Numerical experiments are given which confirm the predictions of our theory.

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M. Holst, M. Licht. 2018-09-27. Geometric Transformation of Finite Element Methods: Theory and Applications. https://arxiv.org/abs/1809.10354

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